Stability of Fredholm Integral Equation of the First Kind in Reproducing Kernel Space

Stability of Fredholm Integral Equation of the First Kind in Reproducing Kernel Space

Year:    2012

Author:    Hong Du, Lihua Mu

Communications in Mathematical Research , Vol. 28 (2012), Iss. 2 : pp. 121–126

Abstract

It is well known that the problem on the stability of the solutions for Fredholm integral equation of the first kind is an ill-posed problem in $C[a, b]$ or $L^2 [a, b]$. In this paper, the representation of the solution for Fredholm integral equation of the first kind is given if it has a unique solution. The stability of the solution is proved in the reproducing kernel space, namely, the measurement errors of the experimental data cannot result in unbounded errors of the true solution. The computation of approximate solution is also stable with respect to $‖·‖_C$ or $‖· ‖_{L^2}$. A numerical experiment shows that the method given in this paper is stable in the reproducing kernel space.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2012-CMR-19051

Communications in Mathematical Research , Vol. 28 (2012), Iss. 2 : pp. 121–126

Published online:    2012-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    6

Keywords:    Freholm integral equation ill-posed problem reproducing kernel space.

Author Details

Hong Du

Lihua Mu